SOLUTION: Solve the exponential equation: 8^x - 3(8^-x) = 2 My answer key says it's x = log(3)/log(8) but I have no idea how to get there

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the exponential equation: 8^x - 3(8^-x) = 2 My answer key says it's x = log(3)/log(8) but I have no idea how to get there      Log On


   

Question 1061338: Solve the exponential equation:
8^x - 3(8^-x) = 2
My answer key says it's x = log(3)/log(8) but I have no idea how to get there
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the exponential equation:
8^x - 3(8^-x) = 2
My answer key says it's x = log(3)/log(8) but I have no idea how to get there
8%5Ex+-+3%288%5E%28-+x%29%29+=+2 =====> 8%5Ex+-+3%281%2F8%5Ex%29+=+2 =====> 8%5Ex+-+3%2F8%5Ex+=+2 =====> 8%5Ex+-+3%2F8%5Ex+-+2+=+0

8%5E%282x%29+-+3+-+2%288%5Ex%29+=+0 ------- Multiplying by LCD, 8%5Ex

8%5E%282x%29+-+2%288%5Ex%29+-+3+=+0

Let a = 8%5Ex

Then, 8%5E%282x%29+-+2%288%5Ex%29+-+3+=+0 becomes: a%5E2+-+2a+-+3+=+0 

(a - 3)(a + 1) = 0

a - 3 = 0      OR         a + 1 = 0

a = 3          OR         a = - 1

Replacing "a" with 8%5Ex

8%5Ex+=+3       OR      8%5Ex+=+-+1

 ------ Converting matrix%281%2C6%2C+8%5Ex%2C+%22=%22%2C+3%2C+to%2C+LOGARITHMIC%2C+form%29



matrix%281%2C3%2C+x%2C+%22=%22%2C+log+%288%2C+-+1%29%29 ------ Converting matrix%281%2C6%2C+8%5Ex%2C+%22=%22%2C+-+1%2C+to%2C+LOGARITHMIC%2C+form%29, but IGNORE this as LOG VALUE CANNOT be < 0 (negative)